You could consider no change as good news for the labor movement, considering the decline in union membership over the past 30 years. In 1983, more than 20 percent of American workers belonged to unions.

AFL-CIO President Richard Trumka said he's encouraged by some union growth in the South,… more

Joshua Roberts/Bloomberg

Since then, the number of union workers has declined from 17.7 million to 14.5 million, even as the the overall size of the American work force grew.

Today, there are nearly just as many public-sector workers in unions as there are private-sector workers. The union membership rate among public-sector workers in 2013 was 35.3 percent, down from 35.9 percent in 2012. The union membership rate for private-sector workers was 6.7 percent, up from 6.6 percent in 2012.

Highly unionized occupations included teachers, police officers and firefighters. In the private sector, union members were most common in utilities, transportation and warehousing, telecommunications, and construction.

New York had the highest union membership rate of any state at 24.4 percent, and North Carolina had the lowest at 3 percent.

Union members made more money than non-union workers: median weekly earnings of $950 compared with $750.

"Along with higher wages, other data show that union members have greater access to employment-based benefits, such as health insurance, a retirement savings plan, and sick and vacation leave," said Secretary of Labor Thomas Perez.

Perez made it clear that he thinks that workers would be better off if more of them join unions.

"The decline in union membership over the last few decades has contributed to more working families struggling to get by," he said. "When workers have a seat at the table, they are better able to bargain for their fair share of the value they helped create; and that leads to greater economic security and economic mobility for everyone. As our economy continues to recover and we work to create good jobs, we need to ensure workers can lift their voices to raise wages, reduce inequality and help more people climb ladders of opportunity."

Meanwhile, AFL-CIO President Richard Trumka saw some signs of hope in the slight growth in the private-sector union membership rate.

"BLS shows encouraging growth in the South from Alabama to Kentucky - but public sector workers remain under attack," Trumka tweeted.

But union leaders like Trumka can't be encouraged by another trend in the BLS data: The younger you are, the less likely you are to be in an union. Only 9.8 percent of workers age 25-34 are union members, compared with 14.3 percent of workers in the 55-64 age range. As these older workers retire, will they be replaced by union members?